EPSY 5356 Principles of Educational and Psychological Measurement

EPSY 5380

INTRODUCTION TO EDUCATIONAL STATISTICS

Credit: 3 Hours Semester: Spring 2002 Instructor: Arturo Olivárez, Jr. Ph. D. Office: AD/ED 334 Office Phone #: (806) 742-1997 x 293 Office Hours: T-W-Th 2:00-5:00 p.m. (or by appointment) E-mail: [email protected] Meeting time: 6:00 –8:50 pm Tuesdays Meeting place: AD/Ed 349

Course Description

Prerequisite: None

The present course has several goals that are intended to help students understand fundamental concepts and methods of statistics as applied to educational and psychological problems. These include: Introduction to basic concepts of descriptive and inferential statistics as they apply to educational and psychological research. Basic and intermediate concepts for testing statistical hypotheses, construction and interpretation of confidence intervals, and applying selected nonparametric techniques will be covered.

Instructional Units

1. An introduction to the different aspects involved in applying statistical concepts to the solution of educational and psychological research questions. These will include the differentiation of populations and samples, descriptive versus inferential statistics, parametric versus nonparametric procedures, and experimental versus statistical research control. Added to these concepts will be the introduction of basic concepts such as parameters and statistics, scales of measurement, and discrete and continuous variables.

2. Overview of frequency distributions and tables, graphs, and distribution shapes. This will include transformation of data into percentiles ranks and Graphical description of frequencies using stem and leaf and box-and-whiskers displays.

3. An overview of the most common measures of central tendency and measures of dispersion. This will include procedures for determining their location and meaning in reference to population and sample distributions.

4. Transformation and utilization of data by using standardized scores and how these relate to the shape of a given distribution.

5. Introduction to basic concepts of probability and how these concepts relate to distributions. This will include the introduction to the concept of sampling distributions for the mean and other statistics and their respective standard errors. 6. Introduction to measures of association to describe pairs of variables under different levels of measurement. Both descriptive and inferential procedures will be described and explained. 7. Introduction to linear regression as it is used in prediction studies. Both descriptive and inferential procedures will be described and explained.

8. An introduction to different statistical procedures used for the solution of questions related to one-group and/or one-sample design including the selection of test of significance and estimation on the mean, correlation index, and proportions.

9. Demonstration for the use of Chi-squared test of significance for homogeneity and independence and the Chi-squared test for two-sample and three-sample cases.

Textbooks and Other Required Reading, Other Instructional Resources

Kirk, Roger E. (1999). Statistics: An Introduction. 4th ed. Hartcourt Brace College Publishers, Fort Worth, TX.

The instructor may also require, on occasion, additional reading from other sources. This may be assigned during the semester.

Evaluation

1. Chapter Quizzes. Thirteen chapter quizzes (multiple choice, short answer, computational problems) will be given for the reviewing of the individual chapters as a self-evaluation tool. Some of these items may be used in the unit examinations so they serve a dual role of reinforcing the learned material. The first quiz will be given at the end of every class meeting. the quizzes are being used as part of the learning-teaching model used by the instructor. The student will turn the completed quiz as part of the chapter’s exercises once the chapter has been covered. Once the chapter has been finished the student will have one week to turn in the completed quiz (Next meeting class). These quizzes will yield a total of 10%.of your final grade.

2. Comprehensive exams. The student will earn a satisfactory grade on four unit exams. The format of the test will include computational problems and conceptual questions. These exams will be in-class emphasizing concepts and computational applications. Some of the sections will include computer and statistical package outputs such as SAS, SPSS, PC versions. Each of the unit exams will count approximately 100 points. These exams will yield a total of 80% of your final grade.

3. Chapter exercises. The student will be assigned problems exercises from each chapter, including computer problems, for credit. The chapter exercises will be assigned after each chapter presentation (See tentative schedule) and are to be turn-in in a timely manner. These problems are worth 10 points. These chapter exercises, along with the chapter quizzes, will be turned in once the chapter material has been covered a week later. Your efforts on this task will yield a total of 10% of the final exam.

Grading summary of course assignments. 13 Chapter quizzes 10% 4 Unit exams 40% 13 Chapter exercises 10% Total 100%

Letter grade assignment (University guidelines)

90.0--93.9 A- 94.0--96.9 A 97.0-99.9 A+ 80.0--83.9 B- 84.0--86.9 B 87.0-89.9 B+ 70.0--73.9 C- 74.0--76.9 C 77.0-79.9 C+ 60.0--63.9 D- 64.0--66.9 D 67.0-69.9 D+ < 60 F

In order to obtain a grade based on the criteria above, all assignments must be completed before the semester is over. If a student fails to complete the assigned tasks, then an incomplete grade, an I, will be posted in the student record. Students are discouraged to place themselves in that position since the grading system changes once the student does not finish the required material for the semester. The grading procedures' changes are left to the discretion of the instructor. Additionally, some rules to follow while enrolled in this course: 1) Absolutely No Extensions Permitted. Late Assignments Will Be Penalized on points losses For Each Late Day. 2) Please be Courteous To Your Classmates and Instructor. See “civility in the class room below” 3) I Reserve The Right to Change Procedures, Readings, And Topics As Necessary, With Ample Warning. 4) If you must miss more than two class meetings, I advise that you take the course at some other time. 5) Class attendance is expected and strongly encouraged. Contact instructor if you have to be absent so that material, assignments and exams missed by student are made up in timely manner.

Civility in the classroom.

Students are expected to assist in maintaining a classroom environment that is conducive to learning. In order to assure that all students have an opportunity to gain from time spent in class, unless otherwise approved by the instructor, students are prohibited from using cellular phones or beepers, eating or drinking in class, making offensive remarks, reading newspapers, sleeping or engaging in any other form of distraction. Ad hominem remarks or disparaging comments about gender, ethnicity, religion, etcetera will not be tolerated. Inappropriate behavior in the classroom shall result in, minimally, a request to leave the class.

American with Disability Act.

The university is committed to the principle that in no aspect of its programs shall there be differences in the treatment of persons because of race, creed, national origin, age, sex, or disability, and that equal opportunity and access to facilities shall be available to all. If you require special accommodations in order to participate, please contact me, as soon as possible for necessary accommodations. The student should present appropriate verification from AcessTECH in the office of the Dean of Students. No requirement exists that accommodation be made prior to completion of this approved university process.

Honor Code.

I take our standards of professional ethics seriously, as I expect all members of the academic community to do. Any form of cheating or plagiarism will result in the receipt of a failing grade for this course. Any paper you submit for this class must not have been submitted for any other class. Resubmission of any paper in this class will result in an "F" grade for that paper. No written work may be submitted for academic credit more than once. If you have any questions about how this may apply to a paper you are considering for this class, please ask. You may work in teams but the your work that is turned in for credit is entirely the fruit of yours effort and time expenditure. TENTATIVE SCHEDULE SPRING 2002

Chapter 1 INTRODUCTION TO STATISTICS Assignments Date

1.1 Introduction Jan. 15 1.2 Studying Statistics 1.3 Basic Concepts 1.4 Describing Characteristics by Numbers 1.5 Historical Development of Statistics 1.6 Summary Even Numbered(9) & quiz Jan. 22

Chapter 2 FREQUENCY DISTRIBUTIONS AND GRAPHS

2.1 Introduction Jan. 23 2.2 Frequency Distributions 2.3 Introduction to Graphs 2.4 Graphs for Qualitative Variables 2.5 Graphs for Quantitative Variables 2.6 Shapes of Distributions 2.7 Misleading Graphs 2.8 Printouts for Three Microcomputer Statistical Packages 2.9 Summary Odd Numbered(16) & quiz Jan. 29

Chapter 3 MEASURES OF CENTRAL TENDENCY

3.1 Introduction Jan. 29 3.2 The Mode 3.3 The Mean 3.4 The Median 3.5 Relative Merits of the Mean, Median, and Mode 3.6 Location of the Mean, Median, and Mode in a Distribution 3.7 Mean of Two or More Means 3.8 More About the Summation Operator 3.9 Printouts for Three Microcomputer Packages 3.10 Summary Even Numbered(11) & quiz Feb. 5

Chapter 4 MEASURES OF DISPERSION, SKEWNESS, AND KURTOSIS

4.1 Introduction to Measures of Dispersion Feb. 5 4.2 Five Measures of Dispersion 4.3 Relative Merits of the Measures of Dispersion 4.4 Dispersion and the Normal Distribution 4.5 Detecting Outliers 4.6 Skewness and Kurtosis 4.7 Equivalence of Deviation and Raw-Score Formulas for a Standard Deviation 4.8 Printouts for Three Microcomputer Packages 4.9 Summary Odd Numbered(11) & quiz Feb 12 Review of the first 4 chapters UNIT TEST # 1 (SECOND HALF OF CLASS TIME) FEB. 12 Chapter 5 CORRELATION

5.1 Introduction to Correlation Feb. 19 5.2 A Numerical Index of Correlation 5.3 Pearson Product-Moment Correlation Coefficient 5.4 Interpretation of a Correlation Coefficient: Explained and Unexplained Variation 5.5 Some Common Errors in Interpreting a Correlation Coefficient 5.6 Factors That Affect the Size of a Correlation Coefficient 5.7 Spearman Rank Correlation 5.8 Other Kinds of Correlation Coefficients 5.9 Printouts for Three Microcomputer Packages 5.10 Summary Even Numbered(14) & quiz Feb. 26

Chapter 6 REGRESSION

6.1 Introduction to Regression Feb. 26-Mar 5 6.2 Criterion for the Line of Best Fit 6.3 Another Measure of Ability to Predict: The Standard Error of Estimate 6.4 Assumptions Associated With Regression and the Standard Error of Estimate 6.5 Multiple Regression and Multiple Correlation 6.6 Printouts for Three Microcomputer Packages 6.7 Summary Odd Numbered(7) & quiz Mar. 6 Review of chapters 5 and 6 and TEST # 2 MAR. 6 (Second part of class time)

SPRING BREAK MAR. 12 Chapter 7 PROBABILITY

7.1 Introduction to Probability Mar. 19 7.2 Basic Concepts 7.3 Probability of Combined Events 7.4 Counting Simple Events 7.5 Summary Even Numbered(12) & quiz Mar. 26

Chapter 8 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS

8.1 Random Sampling Mar. 26 8.2 Random Variables and Their Distributions 8.3 Binomial Distribution 8.4 Summary Odd Numbered(10) & quiz Apr. 2

Chapter 9 NORMAL DISTRIBUTION AND SAMPLING DISTRIBUTIONS

9.1 The Normal Distribution Apr. 2 9.2 Interpreting Scores in Terms of z Scores and Percentile Ranks 9.3 Sampling Distributions 9.4 Summary Even Numbered(10) & quiz Apr. 9 9.5 Supplementary Note Chapter 10 STATISTICAL INFERENCE: ONE SAMPLE

TEST # 3 APRIL 9 10.1 Introduction to Hypothesis Testing April 9 10.2 Hypothesis Testing 10.3 One-Sample z Test for a Mean when the Variance Is Known 10.4 More About Hypothesis Testing 10.5 Confidence Interval for a Mean 10.6 Practical Significance 10.7 Summary Odd Numbered(15) & quiz Apr. 16

Chapter 11 STATISTICAL INFERENCE OTHER ONE-SAMPLE TEST STATISTICS

11.1 Introduction to Other One-Sample Test Statistics Apr. 16 11.2 One-Sample t Test and Confidence Interval for a Mean 11.3 One-Sample Chi-Square Test and Confidence Interval for a Variance 11.4 One-Sample z test and Confidence Interval for a Proportion 11.5 One-Sample t and z Tests and Confidence Interval for a Correlation 11.6 Printouts for Three Microcomputer Packages 11.7 Summary Even Numbered(8) & quiz Apr. 23

Chapter 16 STATISTICAL INFERENCE FOR FREQUENCY DATA

16.1 Three Applications of Pearson’s Chi-Square Statistic Apr. 23 16.2 Testing Goodness of Fit 16.3 Testing Independence 16.4 Testing Equality of c  2 Proportions 16.5 Printouts for Three Microcomputer Packages 16.6 Summary Even Numbered(7)& quiz Apr. 30 16.7 Supplementary Notes

Chapter 17 STATISTICAL INFERENCE FOR RANKED DATA

17.1 Introduction to Assumption-Freer Tests May 1 17.2 Mann-Whitney U Test for Two Independent Samples 17.3 Wilcoxon T Test for Dependent Samples 17.4 Comparison of Parametric Tests and Assumption-Freer Tests for Ranked Data 17.5 Printouts for Three Microcomputer Packages 17.6 Summary Odd numbered(6) & quiz May 7

FINAL EXAM MAY 7 2002 Statistics Bibliography

Bruning, J. L., & Kintz, B. L. (1997). Computational Handbook of Statistics. (4th ed.). New York: Longman.

Cody, R. P. & Smith, J. K., (1997). Applied Statistics and the SAS Programming Language. (4th Ed.). Upper Saddle River, NJ: PrenticeHall.

Edwards, A. L. (1985). Multiple Regression and Analysis of Variance and Covariance. (2nd ed.). W. H. Freeman and Company: New York.

Glass, G. V., & Hopkins, K. D. (1984). Statistical Methods in Education and Psychology, (2nd ed.) New Jersey: Prentice-Hall, Inc.

Keppel, G., & Zedeck. S. (1989). Data Analysis for Research Designs. W. H. Freeman and Company: New York.

Kirk, R. E., (1999). Statistics: An Introduction. (4th. Ed.) Fort Worth, TX: Harcourt Brace College Publishers.

Kirk, R. E. (1995). Experimental Design: Procedures for the Behavioral Sciences. (3rd ed.). Brooks/Cole Publishing Co.

Lehman, P. W. (1988). Statistical Reasoning for the Behavioral Sciences: Study Guide (2nd ed.). Boston: Allyn and Bacon, Inc.

Marascuilo, L. A., & Serlin, R. C. (1988). Statistical Methods for the Social and Behavioral Sciences. W. H. Freeman and Company: New York.

Pedhazur, E. J. (1982). Multiple Regression in Behavioral Science: Explanation and Prediction. (2nd ed.). Holt, Rinehart and Winston: New York.

Roscoe, R. J. (1975). Fundamental Research Statistics for the Behavioral Sciences. New York: Holt, Rinehart, and Winston, Inc.

Shavelson, R. J. (1988). Statistical Reasoning for the Behavioral Sciences (2nd ed.). Boston: Allyn and Bacon, Inc.

Scheaffer, R. L., W. Mendehall, & Ott, L. Elementary Survey Sampling. (4th Ed.) Belmont, CA: Duxbury Press.

Winer, B. J., Brown, D. R., & Michels, K. M. (1991). Statistical Principles in Experimental Design. (3rd ed.). McGraw-Hill, Inc.: New York. EPSY 5380 SPRING SEMESTER 2002 ROSTER

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